A Software Tool for. Automatically Veried Operations on. Intervals and Probability Distributions. Daniel Berleant and Hang Cheng

Size: px
Start display at page:

Download "A Software Tool for. Automatically Veried Operations on. Intervals and Probability Distributions. Daniel Berleant and Hang Cheng"

Transcription

1 A Software Tool for Automatically Veried Operations on Intervals and Probability Distributions Daniel Berleant and Hang Cheng Abstract We describe a software tool for performing automatically veried arithmetic operations on independent operands when the operands are intervals, or probability distribution functions, or one operand is an interval and the other is a distribution. Intervals and distributions are expressed using the same technique, so the algorithms do not need to distinguish between intervals and distributions in their operation. The tool can calculate common arithmetic operations with guaranteed results (as well as condence limits on a distribution if the distribution is empirically estimated from samples). A previous paper (Berleant 1993 [1]) discusses the concepts, algorithms, and related work. Here we emphasize a software tool that implements the algorithms, interacts with the user via a graphical user interface, and saves, retrieves, and prints the results of its calculations. 1 Introduction to the Representation We use histograms to represent, correctly, both probability distribution functions (PDFs) and intervals. We take an interval to be an incompletely specied description of value such that there is a probability of one that the actual but unknown value falls within the interval. A probability distribution may be in the form of either a probability density function (PDF) or its integral, a cumulative distribution function (CDF). Next, we show how to represent both distribution functions and intervals, correctly, using the same representational technique. 1.1 Representing a Distribution Function Histograms are a natural way for people to create and edit probability distributions, and are used for this purpose by our software tool. While a histogram discretizes the underlying PDF, in our technique this discretization introduces 1

2 no error, and thereby maintains correctness. Instead, it introduces information loss. To see this, consider a histogram discretization of a PDF to be a partitioning of the PDF's domain into a set of intervals, each of which is associated with a probability mass equal to the area under the PDF across the range of that interval. The graphical depiction of a histogram is then simply a convention for describing this set of intervals and their associated masses. A histogram graphic (Figure 1) is user friendly but has the disadvantage that a histogram bar is conventionally shown with a at top, which might give the impression that the probability mass associated with the interval for that bar is assumed to be distributed evenly over its range. In fact, in our technique no assumption is made about how the probability mass associated with an interval is distributed over that interval, hence a given histogram bar is consistent with any such distribution, including the PDF that the histogram might have been intended to discretize but also an innite number of others. This is explained in more detail in Berleant (1993 [1]), but the main point to consider is that this view of a histogram allows it to discretize a PDF correctly but with information loss, and displaying the bars with at tops is merely a graphical convention. The more bars in the histogram, the less the information loss. The software tool we report here includes the capability of allowing users to graphically edit histograms. To underline their information-losing but correctness properties, the tool also allows display of the same information in another graphical form, the integral (or cumulated probability) of a histogram. Just as a PDF can be integrated into a corresponding CDF, the histogram discretization of a PDF we have described can also be integrated and this cumulated form displayed graphically (Figure 1). The graphic for the cumulation of the histogram consists of two bounding CDFs. The higher of the two assumes the extreme case where the probability mass associated with each bar of the histogram is concentrated at the low bound of its interval. The lower of the two assumes the other extreme, where each probability mass is concentrated at the high bound of its corresponding interval. Any other of the innite number of distributions consistent with the histogram, when integrated, results in a curve that stays within the two stair-step shaped bounding CDFs exemplied in Figure 1. The space between these bounding CDFs reects the information loss associated with the discretization. 1.2 Representing an Interval An interval is represented in our technique as a histogram with one bar. Since the interval representation of value does not assume any particular distribution of probability mass within the interval, the interval representation is consistent with any PDF whose value is zero outside the bounds of the interval, and with any CDF whose value is zero below the interval and one above it (Figure 2). To represent the interval using bounding CDFs, we must determine the space of CDFs consistent with the interval. The two most extreme CDFs that bound 2

3 3 Figure 1: A histogram edited by a user and its two corresponding CDF bounds (one solid and one dotted).

4 this space are the one that rises faster than any other CDF consistent with the interval, and the one that rises slower than any other CDF consistent with the interval. The one that rises fastest will correspond to the PDF which is an impulse of mass 1 at the interval's low bound (that is, the variable's value is certainly equal to the interval's low bound). Likewise, the one that rises slowest will correspond to the PDF which is an impulse of mass 1 at the interval's high bound. The interval is therefore representable as a family of CDFs whose two bounding CDFs each have one \step." Figure 2 shows an interval and its representation as a bounded family of CDFs; the CDF that bounds this family from above jumps from zero to one at the interval's low bound, and CDF that bounds it from below jumps from zero to one at the interval's high bound. 2 Introduction to Arithmetic Operations The algorithmic approach to performing an arithmetic operation on histograms is exemplied in Figure 3. An arithmetic operation produces as a result a Cartesian product consisting of a set of intervals that in general contains overlaps. Due to the overlaps this set cannot be shown directly as a histogram, but can be integrated and shown correctly as a pair of stepwise, bounding CDFs. (The software tool will however allow a result to be displayed as an approximating histogram if desired, due to the visual impact and intuitive appeal of histograms.) However displayed, this result may in turn be used as an operand in further arithmetic operations. The representational technique of using a set of intervals non-overlapping in the case of PDFs, singleton in the case of an interval operand, and overlapping in the case of results of arithmetic operations and a probability mass associated with each interval in the set, is the key to our algorithm. This representation we term an intermediate distribution and it mediates between PDFs, intervals, and bounding CDFs and is the underlying representation used by the algorithm for its computations. A fuller description of the algorithm is given in Berleant (1993 [1]). Related algorithms appeared beginning in 1968 (Ingram et al. [6]), however these algorithms were not automatically verifying. A recent constraint satisfaction approach to the problem is in Hyvonen (1995 [4]). An approach to using CDF bounds in computer systems administration appears in Post and Diltz (1986 [8]) under the rubric of the stochastic dominance eld, which recognizes the usefulness of bounded families of CDFs. Another area of related work is robust statistics. We have not been able to nd work by others discussing automatically veried operations where one operand is an interval and the other is a distribution function. A fuller review of related work appears in Berleant (1993 [1]). 4

5 5 Figure 2: The interval [4; 7] and its representation as two CDFs bounding the family of all CDFs consistent with the interval.

6 Figure 3a: Let this histogram describe uncertain value X: It depicts the intermediate distribution fp([1; 2]) = 1 2 ; p([2; 4]) = 1 2 g: 6

7 Figure 3b: Let this histogram describe uncertain value Y: It depicts the intermediate distribution fp([2; 3]) = 1 4 ; p([3; 4]) = 1 2 ; p([4; 5]) = 1 4 g: Cartesian product term # #1 #2 #3 #4 #5 #6 interval probability interval probability interval probability interval probability interval probability interval probability Operand 1 (X i) [1; 2] [1; 2] [1; 2] [2; 4] [2; 4] [2; 4] Operand 2 (Y j ) [2; 3] 1=4 [3; 4] [4; 5] 1=4 [2; 3] 1=4 [3; 4] [4; 5] 1=4 Result intermediate distribution [2; 6] 1=8 [3; 8] 1=4 [4; 10] 1=8 [4; 12] 1=8 [6; 16] 1=4 [8; 20] 1=8 Figure 3c: Multiplying the intermediate distributions for X and Y leads to another intermediate distribution, shown in the last column. (This intermediate distribution contains overlapping intervals, as is typical of intermediate distributions resulting from arithmetic operations.) 7

8 Figure 3d: Integrating the result intermediate distribution in the last column of Figure 3c produces these stair-step shaped bounding CDFs. Figure 3 (a-d): Multiplying two operands. The user created two histograms X (Figure 3a) and Y (Figure 3b) using a graphical editor. These histograms are represented internally as intermediate distributions, that is, lists of intervals and associated probability masses. The intermediate distributions are used to calculate X 2 Y, whose intermediate distribution is shown in the last column of Figure 3c. Integrating this result produces the CDF bounds shown in Figure 3d. 3 A Software Tool A software calculating tool that runs under Microsoft Windows has been written. This tool does automatically veried arithmetic operations on operands, each of which may be either an interval or a distribution function. 8

9 3.1 Creating and Displaying Operands The tool allows the user to graphically create and edit histograms using the mouse. A mouse-click based menu can be used to increase or decrease the number of bars in the histogram. Clicking the left button above a bar increases its height (and hence its area, which denes its probability mass) in proportion to how high above the bar the cursor is when the left button is pressed. Clicking the left button below the top of the bar decreases its height analogously. The width of a bar can also be increased or decreased, by clicking the right (instead of the left) mouse button above or below the top of the bar. As an alternative to mouse-based graphical editing, numerical values can be typed in directly when desired, by clicking on the Edit button at the top of the screen (visible e.g. in Figure 1) and invoking a dialog box. Clicking on the File button allows saving a histogram to a disk le, or reading one in from a disk le. The intent is to provide a user interface that is easy-to-use yet quite exible. An input histogram, as well as the result of an arithmetic operation on histogram operands, is represented internally as an intermediate distribution. This set of intervals each associated with a probability mass, when stored on disk, is stored as a list of triples. Each triple species specifying an interval low bound, an interval high bound, and a probability mass for the interval. This list can be edited using an ordinary text editor if desired. All intermediate distributions may be displayed graphically as histograms. These histograms are labeled Approximate when the intermediate distribution has overlapping intervals, as is usually the case for the result of an arithmetic operation. Approximate histograms cannot be edited, and like other histograms can alternatively be displayed correctly (not approximately) as a pair of bounding CDFs. 3.2 Operations on Operands The tool provides several primitive operations. A menu of these operations is invoked by clicking on the Operation button at the top of the screen (Figure 4). Operations in f+; 0; 2; 4g take the top two panels A and B as operands and place the result in the lowest of the three panels, panel C (Figure 5), overwriting anything that may already be in C. If this result is to be used as an operand in a subsequent operation, it may be moved into panel A or B using one of the Exchange operations (Figure 4). An operand or result may be viewed as either a histogram or a pair of CDF bounds and may be viewed in detailed form (e.g. Figure 1), with or without a grid. As an added feature, the tool can apply results of Kolmogorov (1941 [7]) and others to obtain bounds on the CDF for a random variable for which some samples are provided. The samples must be provided in a text le ending in \.smp" and containing their numerical values. This le may be read into panel A and displayed in cumulated form as an empirically estimated CDF for the underlying random variable. Then, the operation C = A's Condence Limits... 9

10 Figure 4: The operations oered by the tool. 10

11 Figure 5: Panel C contains the result of applying an operation (division in this case) to A and B. Panel C, labeled Approximate as displayed in histogram form, can alternatively be exactly displayed as a pair of bounding CDFs. 11

12 Figure 6: Condence limits around the CDF in panel A, if generated from samples of a random variable (several dozen student test scores in this case) may be calculated and shown in panel C. The condence level is chosen from a menu. (Figure 4) may be invoked to place in panel C bounds on the actual but unknown CDF for the random variable, to a given condence level (Figure 6). Various functions of the software tool may be grouped together and partially automated using a primitive batch command facility. 4 Future Work We now have a tool for doing common arithmetic operations on distribution function and interval operands. However, much more remains to be done to extend and apply the work. A next major stage in the research is to identify applications and apply the tool to those applications. Once identied, an application can serve not only to demonstrate the practical value of an idea but also to guide its further extension. Digital signal processing and highway maintenance decision support are among 12

13 those that have been suggested. Applications of stochastic dominance are also possible candidates, as are applications of robust statistics. The world is full of incompletely known values which need to be taken into account, underlining the importance and potential value of research dealing with incompletely known information. A number of extensions to the tool described here would be useful: Handling calculations whose intermediate results are dependent on one another could be done by implementing not only the common arithmetic operations as we have done, but also combinations of those so that, for example, given histograms in panels A and B; (B 0 A)=A could be calculated even though (B 0A) and A are dependent on each other. This would require a simple expression parser and, although excess width might occur in constituent interval calculations in many cases, the result would still be correct (Berleant 1993 [1]). Providing exponentiation, logarithms, trigonometric and other unary and binary operations would be useful. Handling distribution functions that have tails extending out to innite could be handled by applying the work of others on handling intervals containing bounds of 1 and 01: The tool is presently modeled after a calculator, in which only a small number of operands can be handled at once. A useful extension to the calculator concept is the spreadsheet concept. Interval mathematics has been implemented in spreadsheets (Hyvonen 1994 [5]) and distribution functions have also been shown to be feasible as cells in spreadsheets in commercial products such as Crystal Ball [3] [9]. 5 Conclusion The present paper describes a computer tool with graphical user interface capabilities, for allowing users to specify interval and distribution function operands as histograms and allowing them to perform automatically veried arithmetic operations on those operands. A previous paper (Berleant 1993 [1]) reviews related work and describes in more detail how automatically veried arithmetic operations may be carried out on intervals and distribution functions. An important next stage in this research is to nd applications for the techniques in order to demonstrate practical use of the tool and its underlying ideas. Details on the implementation appear in Cheng (1994 [2]). The software is available at no charge (for non-commercial purposes) from the authors. 13

14 6 Acknowledgements We thank Robert Babcock for helping to facilite support for one of the authors (Cheng), Vladik Kreinovich for his encouragement, Dan Layne for originally suggesting the interval mathematics forums, and Bill Walster for suggesting some possible application directions. References [1] D. Berleant, \Automatically Veried Reasoning with Both Intervals and Probability Density Functions," Interval Computations, 1993 No. 2, pp. 48{ 70. [2] H. Cheng, \A Software Tool for Automatically Veried Reasoning with Intervals and Cumulative Distribution Functions," Master's Thesis, Dept. of Computer Systems Engineering, U. of Arkansas, Fayetteville, Dec [3] Crystal Ball, software product, Decisioneering Inc., 1380 Lawrence St. Suite 520, Denver CO [4] E. Hyvonen, \Constraint Reasoning on Probability Distributions," manuscript (1995), author is at VTT Information Technology, P.O. Box 1201, VTT, FINLAND, [5] E. Hyvonen, \Spreadsheets Based on Interval Constraint Satisfaction," Articial Intelligence for Engineering Design, Analysis, and Manufacturing, Vol. 8, 1994, pp. 27{34. [6] G. E. Ingram, E. L. Welker, and C. R. Herrmann, \Designing for Reliability Based on Probabilistic Modeling Using Remote Access Computer Systems," Proceedings 7th Reliability and Maintainability Conference, American Society of Mechanical Engineers, 1968, pp. 492{500. [7] A. Kolmogoro (a.k.a. Kolmogorov), \Condence Limits for an Unknown Distribution Function," Annals of Mathematical Statistics, Vol. 12, No. 4, 1941, pp [8] G. V. Post and J. D. Diltz, \A Stochastic Dominance Approach to Risk Analysis of Computer Systems," Management Information Systems Quarterly, Vol. 10, No. 4, Dec. 1986, pp. 363{375. software product, Palisade Corp., 31 Decker Rd., Neweld, NY

15 Contact: Daniel Berleant Dept. of Computer Systems Engineering University of Arkansas Fayetteville, AR

Spreadsheet - Introduction

Spreadsheet - Introduction CSCA0102 IT and Business Applications Chapter 6 Spreadsheet - Introduction Spreadsheet A spreadsheet (or spreadsheet program) is software that permits numerical data to be used and to perform automatic

More information

Access 2007 Creating Forms Table of Contents

Access 2007 Creating Forms Table of Contents Access 2007 Creating Forms Table of Contents CREATING FORMS IN ACCESS 2007... 3 UNDERSTAND LAYOUT VIEW AND DESIGN VIEW... 3 LAYOUT VIEW... 3 DESIGN VIEW... 3 UNDERSTAND CONTROLS... 4 BOUND CONTROL... 4

More information

To create a histogram, you must organize the data in two columns on the worksheet. These columns must contain the following data:

To create a histogram, you must organize the data in two columns on the worksheet. These columns must contain the following data: You can analyze your data and display it in a histogram (a column chart that displays frequency data) by using the Histogram tool of the Analysis ToolPak. This data analysis add-in is available when you

More information

Creating and Using Links and Bookmarks in PDF Documents

Creating and Using Links and Bookmarks in PDF Documents Creating and Using Links and Bookmarks in PDF Documents After making a document into a PDF, there may be times when you will need to make links or bookmarks within that PDF to aid navigation through the

More information

Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay

Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture - 17 Shannon-Fano-Elias Coding and Introduction to Arithmetic Coding

More information

Preface of Excel Guide

Preface of Excel Guide Preface of Excel Guide The use of spreadsheets in a course designed primarily for business and social science majors can enhance the understanding of the underlying mathematical concepts. In addition,

More information

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques

More information

A Monte Carlo Simulation Method for the Assessment of Undiscovered, Conventional Oil and Gas

A Monte Carlo Simulation Method for the Assessment of Undiscovered, Conventional Oil and Gas Chapter 3 A Monte Carlo Simulation Method for the Assessment of Undiscovered, Conventional Oil and Gas By Ronald R. Charpentier and T.R. Klett Chapter 3 of Jurassic-Cretaceous Composite Total Petroleum

More information

VISUALIZATION OF DENSITY FUNCTIONS WITH GEOGEBRA

VISUALIZATION OF DENSITY FUNCTIONS WITH GEOGEBRA VISUALIZATION OF DENSITY FUNCTIONS WITH GEOGEBRA Csilla Csendes University of Miskolc, Hungary Department of Applied Mathematics ICAM 2010 Probability density functions A random variable X has density

More information

Excel Guide for Finite Mathematics and Applied Calculus

Excel Guide for Finite Mathematics and Applied Calculus Excel Guide for Finite Mathematics and Applied Calculus Revathi Narasimhan Kean University A technology guide to accompany Mathematical Applications, 6 th Edition Applied Calculus, 2 nd Edition Calculus:

More information

Intro to Excel spreadsheets

Intro to Excel spreadsheets Intro to Excel spreadsheets What are the objectives of this document? The objectives of document are: 1. Familiarize you with what a spreadsheet is, how it works, and what its capabilities are; 2. Using

More information

Introduction to SAS Business Intelligence/Enterprise Guide Alex Dmitrienko, Ph.D., Eli Lilly and Company, Indianapolis, IN

Introduction to SAS Business Intelligence/Enterprise Guide Alex Dmitrienko, Ph.D., Eli Lilly and Company, Indianapolis, IN Paper TS600 Introduction to SAS Business Intelligence/Enterprise Guide Alex Dmitrienko, Ph.D., Eli Lilly and Company, Indianapolis, IN ABSTRACT This paper provides an overview of new SAS Business Intelligence

More information

Access Tutorial 8: Combo Box Controls

Access Tutorial 8: Combo Box Controls Access Tutorial 8: Combo Box Controls 8.1 Introduction: What is a combo box? So far, the only kind of control you have used on your forms has been the text box. However, Access provides other controls

More information

Drawing a histogram using Excel

Drawing a histogram using Excel Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to

More information

Statistics Revision Sheet Question 6 of Paper 2

Statistics Revision Sheet Question 6 of Paper 2 Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of

More information

Client Database chapter4page 1 of 15

Client Database chapter4page 1 of 15 Client Database chapter4page 1 of 15 Client Database Tutorial This database module is for use with the following programs from AbbottSoft I-Rent Software I-Sell POS Software XPressSell POS Software QuickFix

More information

Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools. Tools for Summarizing Data Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

More information

Understanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation

Understanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation Understanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation Leslie Chandrakantha lchandra@jjay.cuny.edu Department of Mathematics & Computer Science John Jay College of

More information

Creating A Grade Sheet With Microsoft Excel

Creating A Grade Sheet With Microsoft Excel Creating A Grade Sheet With Microsoft Excel Microsoft Excel serves as an excellent tool for tracking grades in your course. But its power is not limited to its ability to organize information in rows and

More information

Advanced Microsoft Excel 2010

Advanced Microsoft Excel 2010 Advanced Microsoft Excel 2010 Table of Contents THE PASTE SPECIAL FUNCTION... 2 Paste Special Options... 2 Using the Paste Special Function... 3 ORGANIZING DATA... 4 Multiple-Level Sorting... 4 Subtotaling

More information

MS Access Lab 2. Topic: Tables

MS Access Lab 2. Topic: Tables MS Access Lab 2 Topic: Tables Summary Introduction: Tables, Start to build a new database Creating Tables: Datasheet View, Design View Working with Data: Sorting, Filtering Help on Tables Introduction

More information

Working with Excel in Origin

Working with Excel in Origin Working with Excel in Origin Limitations When Working with Excel in Origin To plot your workbook data in Origin, you must have Excel version 7 (Microsoft Office 95) or later installed on your computer

More information

Appendix 2.1 Tabular and Graphical Methods Using Excel

Appendix 2.1 Tabular and Graphical Methods Using Excel Appendix 2.1 Tabular and Graphical Methods Using Excel 1 Appendix 2.1 Tabular and Graphical Methods Using Excel The instructions in this section begin by describing the entry of data into an Excel spreadsheet.

More information

JustClust User Manual

JustClust User Manual JustClust User Manual Contents 1. Installing JustClust 2. Running JustClust 3. Basic Usage of JustClust 3.1. Creating a Network 3.2. Clustering a Network 3.3. Applying a Layout 3.4. Saving and Loading

More information

Exploratory Spatial Data Analysis

Exploratory Spatial Data Analysis Exploratory Spatial Data Analysis Part II Dynamically Linked Views 1 Contents Introduction: why to use non-cartographic data displays Display linking by object highlighting Dynamic Query Object classification

More information

contentaccess Analysis Tool Manual

contentaccess Analysis Tool Manual contentaccess Analysis Tool Manual OCTOBER 13, 2015 TECH-ARROW A.S. Kazansk√° 5, Bratislava 821 05, Slovakia, EU Contents Description of contentaccess Analysis Tool... 2 contentaccess Analysis Tool requirements...

More information

Chapter 3 RANDOM VARIATE GENERATION

Chapter 3 RANDOM VARIATE GENERATION Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.

More information

Figure 1. An embedded chart on a worksheet.

Figure 1. An embedded chart on a worksheet. 8. Excel Charts and Analysis ToolPak Charts, also known as graphs, have been an integral part of spreadsheets since the early days of Lotus 1-2-3. Charting features have improved significantly over the

More information

NIS-Elements: Using Regions of Interest (ROIs) & ROI Statistics

NIS-Elements: Using Regions of Interest (ROIs) & ROI Statistics NIS-Elements: Using Regions of Interest (ROIs) & ROI Statistics Various ROI tools and functions NIS-Elements has several ROI functions designed for data analysis and image quantification. ROIs are a core

More information

6 3 The Standard Normal Distribution

6 3 The Standard Normal Distribution 290 Chapter 6 The Normal Distribution Figure 6 5 Areas Under a Normal Distribution Curve 34.13% 34.13% 2.28% 13.59% 13.59% 2.28% 3 2 1 + 1 + 2 + 3 About 68% About 95% About 99.7% 6 3 The Distribution Since

More information

Directions for Frequency Tables, Histograms, and Frequency Bar Charts

Directions for Frequency Tables, Histograms, and Frequency Bar Charts Directions for Frequency Tables, Histograms, and Frequency Bar Charts Frequency Distribution Quantitative Ungrouped Data Dataset: Frequency_Distributions_Graphs-Quantitative.sav 1. Open the dataset containing

More information

Creating Fill-able Forms using Acrobat 8.0: Part 1

Creating Fill-able Forms using Acrobat 8.0: Part 1 Creating Fill-able Forms using Acrobat 8.0: Part 1 The first step in creating a fill-able form in Adobe Acrobat is to generate the form with all its formatting in a program such as Microsoft Word. Then

More information

CHARTS AND GRAPHS INTRODUCTION USING SPSS TO DRAW GRAPHS SPSS GRAPH OPTIONS CAG08

CHARTS AND GRAPHS INTRODUCTION USING SPSS TO DRAW GRAPHS SPSS GRAPH OPTIONS CAG08 CHARTS AND GRAPHS INTRODUCTION SPSS and Excel each contain a number of options for producing what are sometimes known as business graphics - i.e. statistical charts and diagrams. This handout explores

More information

ABSTRACT INTRODUCTION EXERCISE 1: EXPLORING THE USER INTERFACE GRAPH GALLERY

ABSTRACT INTRODUCTION EXERCISE 1: EXPLORING THE USER INTERFACE GRAPH GALLERY Statistical Graphics for Clinical Research Using ODS Graphics Designer Wei Cheng, Isis Pharmaceuticals, Inc., Carlsbad, CA Sanjay Matange, SAS Institute, Cary, NC ABSTRACT Statistical graphics play an

More information

Call Centre Helper - Forecasting Excel Template

Call Centre Helper - Forecasting Excel Template Call Centre Helper - Forecasting Excel Template This is a monthly forecaster, and to use it you need to have at least 24 months of data available to you. Using the Forecaster Open the spreadsheet and enable

More information

EmpCenter Employee Training for Harvey Mudd College. TR-01: Time and Attendance Employee Functions

EmpCenter Employee Training for Harvey Mudd College. TR-01: Time and Attendance Employee Functions ` EmpCenter Employee Training for Harvey Mudd College TR-01: Time and Attendance Employee Functions LEGAL NOTICES Copyright 2012 WorkForce Software All Rights Reserved. WorkForce Software 38705 Seven Mile

More information

Plotting Data with Microsoft Excel

Plotting Data with Microsoft Excel Plotting Data with Microsoft Excel Here is an example of an attempt to plot parametric data in a scientifically meaningful way, using Microsoft Excel. This example describes an experience using the Office

More information

Handout: Access 2010: Creating Forms

Handout: Access 2010: Creating Forms Access 2010: Creating Forms Table of Contents INTRODUCTION TO FORMS... 4 CREATE A FORM BY USING THE FORM TOOL... 4 CREATE A SPLIT FORM BY USING THE SPLIT FORM TOOL... 4 CREATE A FORM THAT DISPLAYS MULTIPLE

More information

Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information.

Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Excel Tutorial Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Working with Data Entering and Formatting Data Before entering data

More information

Introduction to Statistical Computing in Microsoft Excel By Hector D. Flores; hflores@rice.edu, and Dr. J.A. Dobelman

Introduction to Statistical Computing in Microsoft Excel By Hector D. Flores; hflores@rice.edu, and Dr. J.A. Dobelman Introduction to Statistical Computing in Microsoft Excel By Hector D. Flores; hflores@rice.edu, and Dr. J.A. Dobelman Statistics lab will be mainly focused on applying what you have learned in class with

More information

WEEK #22: PDFs and CDFs, Measures of Center and Spread

WEEK #22: PDFs and CDFs, Measures of Center and Spread WEEK #22: PDFs and CDFs, Measures of Center and Spread Goals: Explore the effect of independent events in probability calculations. Present a number of ways to represent probability distributions. Textbook

More information

WEB TRADER USER MANUAL

WEB TRADER USER MANUAL WEB TRADER USER MANUAL Web Trader... 2 Getting Started... 4 Logging In... 5 The Workspace... 6 Main menu... 7 File... 7 Instruments... 8 View... 8 Quotes View... 9 Advanced View...11 Accounts View...11

More information

Site Maintenance. Table of Contents

Site Maintenance. Table of Contents Site Maintenance Table of Contents Adobe Contribute How to Install... 1 Publisher and Editor Roles... 1 Editing a Page in Contribute... 2 Designing a Page... 4 Publishing a Draft... 7 Common Problems...

More information

APPLYING BENFORD'S LAW This PDF contains step-by-step instructions on how to apply Benford's law using Microsoft Excel, which is commonly used by

APPLYING BENFORD'S LAW This PDF contains step-by-step instructions on how to apply Benford's law using Microsoft Excel, which is commonly used by APPLYING BENFORD'S LAW This PDF contains step-by-step instructions on how to apply Benford's law using Microsoft Excel, which is commonly used by internal auditors around the world in their day-to-day

More information

Software for Agilent Technologies Vector Series Network Analyzers

Software for Agilent Technologies Vector Series Network Analyzers Using the Software Software for Agilent Technologies Vector Series Network Analyzers Software Overview The IntuiLink Vector Series Network Analyzer (VNA) software offers a set of connectivity tools that

More information

Analyzing financial data

Analyzing financial data LESSON 9 Analyzing financial data 9 Lesson objectives, 240 Supporting materials, 238 Instructor preparation, 238 To start this lesson, 240 Reports and graphs help you understand your business, 241 Creating

More information

Statistical Analysis Using Gnumeric

Statistical Analysis Using Gnumeric Statistical Analysis Using Gnumeric There are many software packages that will analyse data. For casual analysis, a spreadsheet may be an appropriate tool. Popular spreadsheets include Microsoft Excel,

More information

understand how image maps can enhance a design and make a site more interactive know how to create an image map easily with Dreamweaver

understand how image maps can enhance a design and make a site more interactive know how to create an image map easily with Dreamweaver LESSON 3: ADDING IMAGE MAPS, ANIMATION, AND FORMS CREATING AN IMAGE MAP OBJECTIVES By the end of this part of the lesson you will: understand how image maps can enhance a design and make a site more interactive

More information

CXQuotes Doors and Windows Quotation software. Cogitrix

CXQuotes Doors and Windows Quotation software. Cogitrix CXQuotes Doors and Windows Quotation software Cogitrix Table of content TABLE OF CONTENT... 2 TABLES OF PICTURES... 6 SOFTWARE FEATURES... 7 QUICK...7 REDUCING ERRORS...7 PRINT QUALITY...7 PRICES COMPARISON...7

More information

Data exploration with Microsoft Excel: univariate analysis

Data exploration with Microsoft Excel: univariate analysis Data exploration with Microsoft Excel: univariate analysis Contents 1 Introduction... 1 2 Exploring a variable s frequency distribution... 2 3 Calculating measures of central tendency... 16 4 Calculating

More information

Ansur Test Executive. Users Manual

Ansur Test Executive. Users Manual Ansur Test Executive Users Manual April 2008 2008 Fluke Corporation, All rights reserved. All product names are trademarks of their respective companies Table of Contents 1 Introducing Ansur... 4 1.1 About

More information

4 Other useful features on the course web page. 5 Accessing SAS

4 Other useful features on the course web page. 5 Accessing SAS 1 Using SAS outside of ITCs Statistical Methods and Computing, 22S:30/105 Instructor: Cowles Lab 1 Jan 31, 2014 You can access SAS from off campus by using the ITC Virtual Desktop Go to https://virtualdesktopuiowaedu

More information

SECTION 2-1: OVERVIEW SECTION 2-2: FREQUENCY DISTRIBUTIONS

SECTION 2-1: OVERVIEW SECTION 2-2: FREQUENCY DISTRIBUTIONS SECTION 2-1: OVERVIEW Chapter 2 Describing, Exploring and Comparing Data 19 In this chapter, we will use the capabilities of Excel to help us look more carefully at sets of data. We can do this by re-organizing

More information

Task Force on Technology / EXCEL

Task Force on Technology / EXCEL Task Force on Technology EXCEL Basic terminology Spreadsheet A spreadsheet is an electronic document that stores various types of data. There are vertical columns and horizontal rows. A cell is where the

More information

An Application of Visual Cryptography To Financial Documents

An Application of Visual Cryptography To Financial Documents An Application of Visual Cryptography To Financial Documents L. W. Hawkes, A. Yasinsac, C. Cline Security and Assurance in Information Technology Laboratory Computer Science Department Florida State University

More information

Tracking Project Progress

Tracking Project Progress L E S S O N 2 Tracking Project Progress Suggested lesson time 45-55 minutes Lesson objectives To begin tracking an active project, you will: a b c Modify the environment for tracking. You will use the

More information

Using Spreadsheets, Selection Sets, and COGO Controls

Using Spreadsheets, Selection Sets, and COGO Controls Using Spreadsheets, Selection Sets, and COGO Controls Contents About this tutorial... 3 Step 1. Open the project... 3 Step 2. View spreadsheets... 4 Step 3. Create a selection set... 10 Step 4. Work with

More information

Data Mining: Exploring Data. Lecture Notes for Chapter 3. Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler

Data Mining: Exploring Data. Lecture Notes for Chapter 3. Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler Data Mining: Exploring Data Lecture Notes for Chapter 3 Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler Topics Exploratory Data Analysis Summary Statistics Visualization What is data exploration?

More information

1. Go to your programs menu and click on Microsoft Excel.

1. Go to your programs menu and click on Microsoft Excel. Elementary Statistics Computer Assignment 1 Using Microsoft EXCEL 2003, follow the steps below. For Microsoft EXCEL 2007 instructions, go to the next page. For Microsoft 2010 and 2007 instructions with

More information

Basic Excel Handbook

Basic Excel Handbook 2 5 2 7 1 1 0 4 3 9 8 1 Basic Excel Handbook Version 3.6 May 6, 2008 Contents Contents... 1 Part I: Background Information...3 About This Handbook... 4 Excel Terminology... 5 Excel Terminology (cont.)...

More information

Exploratory Data Analysis

Exploratory Data Analysis Exploratory Data Analysis Johannes Schauer johannes.schauer@tugraz.at Institute of Statistics Graz University of Technology Steyrergasse 17/IV, 8010 Graz www.statistics.tugraz.at February 12, 2008 Introduction

More information

January 26, 2009 The Faculty Center for Teaching and Learning

January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i

More information

Economic Scenario Generator Version 7 Release Notes

Economic Scenario Generator Version 7 Release Notes Economic Scenario Generator Version 7 Release Notes These release notes describe the changes to the Academy s Economic Scenario Generator that are included in version 7. This release includes updated versions

More information

Word 2010: Mail Merge to Email with Attachments

Word 2010: Mail Merge to Email with Attachments Word 2010: Mail Merge to Email with Attachments Table of Contents TO SEE THE SECTION FOR MACROS, YOU MUST TURN ON THE DEVELOPER TAB:... 2 SET REFERENCE IN VISUAL BASIC:... 2 CREATE THE MACRO TO USE WITHIN

More information

Maple Quick Start. Introduction. Talking to Maple. Using [ENTER] 3 (2.1)

Maple Quick Start. Introduction. Talking to Maple. Using [ENTER] 3 (2.1) Introduction Maple Quick Start In this introductory course, you will become familiar with and comfortable in the Maple environment. You will learn how to use context menus, task assistants, and palettes

More information

MultiQuant Software 2.0 for Targeted Protein / Peptide Quantification

MultiQuant Software 2.0 for Targeted Protein / Peptide Quantification MultiQuant Software 2.0 for Targeted Protein / Peptide Quantification Gold Standard for Quantitative Data Processing Because of the sensitivity, selectivity, speed and throughput at which MRM assays can

More information

A Comparative Study of the Pickup Method and its Variations Using a Simulated Hotel Reservation Data

A Comparative Study of the Pickup Method and its Variations Using a Simulated Hotel Reservation Data A Comparative Study of the Pickup Method and its Variations Using a Simulated Hotel Reservation Data Athanasius Zakhary, Neamat El Gayar Faculty of Computers and Information Cairo University, Giza, Egypt

More information

CONTENTM WEBSITE MANAGEMENT SYSTEM. Getting Started Guide

CONTENTM WEBSITE MANAGEMENT SYSTEM. Getting Started Guide CONTENTM WEBSITE MANAGEMENT SYSTEM Getting Started Guide Table of Contents CONTENTM WEBSITE MANAGEMENT SYSTEM... 1 GETTING TO KNOW YOUR SITE...5 PAGE STRUCTURE...5 Templates...5 Menus...5 Content Areas...5

More information

A Picture Really Is Worth a Thousand Words

A Picture Really Is Worth a Thousand Words 4 A Picture Really Is Worth a Thousand Words Difficulty Scale (pretty easy, but not a cinch) What you ll learn about in this chapter Why a picture is really worth a thousand words How to create a histogram

More information

Clustering & Visualization

Clustering & Visualization Chapter 5 Clustering & Visualization Clustering in high-dimensional databases is an important problem and there are a number of different clustering paradigms which are applicable to high-dimensional data.

More information

Functions & Data Analysis Tools

Functions & Data Analysis Tools Functions & Data Analysis Tools Academic Computing Services www.ku.edu/acs Abstract: This workshop focuses on the functions and data analysis tools of Microsoft Excel. Topics included are the function

More information

GeoGebra Statistics and Probability

GeoGebra Statistics and Probability GeoGebra Statistics and Probability Project Maths Development Team 2013 www.projectmaths.ie Page 1 of 24 Index Activity Topic Page 1 Introduction GeoGebra Statistics 3 2 To calculate the Sum, Mean, Count,

More information

TRADEMARKS. Honeywell is a registered trademark of Honeywell International Inc. All other trademarks are the properties of their respective owners.

TRADEMARKS. Honeywell is a registered trademark of Honeywell International Inc. All other trademarks are the properties of their respective owners. My Keypad for Cell Phones Quick Start Guide 800-02577-CP 12/09 Rev. B TRADEMARKS Honeywell is a registered trademark of Honeywell International Inc. All other trademarks are the properties of their respective

More information

WHO STEPS Surveillance Support Materials. STEPS Epi Info Training Guide

WHO STEPS Surveillance Support Materials. STEPS Epi Info Training Guide STEPS Epi Info Training Guide Department of Chronic Diseases and Health Promotion World Health Organization 20 Avenue Appia, 1211 Geneva 27, Switzerland For further information: www.who.int/chp/steps WHO

More information

IT462 Lab 5: Clustering with MS SQL Server

IT462 Lab 5: Clustering with MS SQL Server IT462 Lab 5: Clustering with MS SQL Server This lab should give you the chance to practice some of the data mining techniques you've learned in class. Preliminaries: For this lab, you will use the SQL

More information

Analysis of Uncertain Data: Tools for Representation and Processing

Analysis of Uncertain Data: Tools for Representation and Processing Analysis of Uncertain Data: Tools for Representation and Processing Bin Fu binf@cs.cmu.edu Eugene Fink e.fink@cs.cmu.edu Jaime G. Carbonell jgc@cs.cmu.edu Abstract We present initial work on a general-purpose

More information

University of Arkansas Libraries ArcGIS Desktop Tutorial. Section 2: Manipulating Display Parameters in ArcMap. Symbolizing Features and Rasters:

University of Arkansas Libraries ArcGIS Desktop Tutorial. Section 2: Manipulating Display Parameters in ArcMap. Symbolizing Features and Rasters: : Manipulating Display Parameters in ArcMap Symbolizing Features and Rasters: Data sets that are added to ArcMap a default symbology. The user can change the default symbology for their features (point,

More information

IBM SPSS Direct Marketing 23

IBM SPSS Direct Marketing 23 IBM SPSS Direct Marketing 23 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 23, release

More information

TABLE OF CONTENTS. INTRODUCTION... 5 Advance Concrete... 5 Where to find information?... 6 INSTALLATION... 7 STARTING ADVANCE CONCRETE...

TABLE OF CONTENTS. INTRODUCTION... 5 Advance Concrete... 5 Where to find information?... 6 INSTALLATION... 7 STARTING ADVANCE CONCRETE... Starting Guide TABLE OF CONTENTS INTRODUCTION... 5 Advance Concrete... 5 Where to find information?... 6 INSTALLATION... 7 STARTING ADVANCE CONCRETE... 7 ADVANCE CONCRETE USER INTERFACE... 7 Other important

More information

Using Excel for Data Manipulation and Statistical Analysis: How-to s and Cautions

Using Excel for Data Manipulation and Statistical Analysis: How-to s and Cautions 2010 Using Excel for Data Manipulation and Statistical Analysis: How-to s and Cautions This document describes how to perform some basic statistical procedures in Microsoft Excel. Microsoft Excel is spreadsheet

More information

Getting Started with Excel 2008. Table of Contents

Getting Started with Excel 2008. Table of Contents Table of Contents Elements of An Excel Document... 2 Resizing and Hiding Columns and Rows... 3 Using Panes to Create Spreadsheet Headers... 3 Using the AutoFill Command... 4 Using AutoFill for Sequences...

More information

BAR CODE 2 OF 5 INTERLEAVED

BAR CODE 2 OF 5 INTERLEAVED ELFRING FONTS INC BAR CODE 2 OF 5 INTERLEAVED This package includes 25 bar code 2 of 5 interleaved fonts in TrueType and PostScript formats, a Windows utility, Bar25i.exe, to help make your bar codes,

More information

GeoGebra. 10 lessons. Gerrit Stols

GeoGebra. 10 lessons. Gerrit Stols GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter

More information

Gestation Period as a function of Lifespan

Gestation Period as a function of Lifespan This document will show a number of tricks that can be done in Minitab to make attractive graphs. We work first with the file X:\SOR\24\M\ANIMALS.MTP. This first picture was obtained through Graph Plot.

More information

Table Of Contents. System Monitoring... 14 System Monitoring Display...14 Monitoring Zones...15 About Areas (partitions)...15 Area Status Display...

Table Of Contents. System Monitoring... 14 System Monitoring Display...14 Monitoring Zones...15 About Areas (partitions)...15 Area Status Display... Quick Start Table Of Contents Getting Started... 2 NEware Editions...2 Installing NEware...3 Installing Languages...3 Connecting to NEware...3 Changing Your IP100 Password...4 User Codes... 5 Master Feature...5

More information

Chapter 32 Histograms and Bar Charts. Chapter Table of Contents VARIABLES...470 METHOD...471 OUTPUT...472 REFERENCES...474

Chapter 32 Histograms and Bar Charts. Chapter Table of Contents VARIABLES...470 METHOD...471 OUTPUT...472 REFERENCES...474 Chapter 32 Histograms and Bar Charts Chapter Table of Contents VARIABLES...470 METHOD...471 OUTPUT...472 REFERENCES...474 467 Part 3. Introduction 468 Chapter 32 Histograms and Bar Charts Bar charts are

More information

One-Minute Spotlight. The Crystal Ball Forecast Chart

One-Minute Spotlight. The Crystal Ball Forecast Chart The Crystal Ball Forecast Chart Once you have run a simulation with Oracle s Crystal Ball, you can view several charts to help you visualize, understand, and communicate the simulation results. This Spotlight

More information

ModelRisk for Insurance and Finance. Quick Start Guide

ModelRisk for Insurance and Finance. Quick Start Guide ModelRisk for Insurance and Finance Quick Start Guide Copyright 2008 by Vose Software BVBA, All rights reserved. Vose Software Iepenstraat 98 9000 Gent, Belgium www.vosesoftware.com ModelRisk is owned

More information

UNICORN 7.0. Administration and Technical Manual

UNICORN 7.0. Administration and Technical Manual UNICORN 7.0 Administration and Technical Manual Page intentionally left blank Table of Contents Table of Contents 1 Introduction... 1.1 Administrator functions overview... 1.2 Network terms and concepts...

More information

IBM SPSS Direct Marketing 22

IBM SPSS Direct Marketing 22 IBM SPSS Direct Marketing 22 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 22, release

More information

Writer Guide. Chapter 15 Using Forms in Writer

Writer Guide. Chapter 15 Using Forms in Writer Writer Guide Chapter 15 Using Forms in Writer Copyright This document is Copyright 2005 2008 by its contributors as listed in the section titled Authors. You may distribute it and/or modify it under the

More information

bbc Creating a Purchase Order Form Adobe LiveCycle Designer ES2 November 2009 Version 9

bbc Creating a Purchase Order Form Adobe LiveCycle Designer ES2 November 2009 Version 9 bbc Adobe LiveCycle Designer ES2 November 2009 Version 9 2009 Adobe Systems Incorporated. All rights reserved. Adobe LiveCycle Designer ES2 (9.0) for Microsoft Windows November 2009 This tutorial is licensed

More information

Variable: characteristic that varies from one individual to another in the population

Variable: characteristic that varies from one individual to another in the population Goals: Recognize variables as: Qualitative or Quantitative Discrete Continuous Study Ch. 2.1, # 1 13 : Prof. G. Battaly, Westchester Community College, NY Study Ch. 2.1, # 1 13 Variable: characteristic

More information

Technology WHITE PAPER

Technology WHITE PAPER Technology WHITE PAPER What We Do Neota Logic builds software with which the knowledge of experts can be delivered in an operationally useful form as applications embedded in business systems or consulted

More information

An Introduction to SPSS. Workshop Session conducted by: Dr. Cyndi Garvan Grace-Anne Jackman

An Introduction to SPSS. Workshop Session conducted by: Dr. Cyndi Garvan Grace-Anne Jackman An Introduction to SPSS Workshop Session conducted by: Dr. Cyndi Garvan Grace-Anne Jackman Topics to be Covered Starting and Entering SPSS Main Features of SPSS Entering and Saving Data in SPSS Importing

More information

DecisionSpace Earth Modeling Software

DecisionSpace Earth Modeling Software DATA SHEET DecisionSpace Earth Modeling Software overview DecisionSpace Geosciences Flow simulation-ready 3D grid construction with seamless link to dynamic simulator Comprehensive and intuitive geocellular

More information

LEGENDplex Data Analysis Software

LEGENDplex Data Analysis Software LEGENDplex Data Analysis Software Version 7.0 User Guide Copyright 2013-2014 VigeneTech. All rights reserved. Contents Introduction... 1 Lesson 1 - The Workspace... 2 Lesson 2 Quantitative Wizard... 3

More information

Using Excel for Statistical Analysis

Using Excel for Statistical Analysis 2010 Using Excel for Statistical Analysis Microsoft Excel is spreadsheet software that is used to store information in columns and rows, which can then be organized and/or processed. Excel is a powerful

More information

Creating a Participants Mailing and/or Contact List:

Creating a Participants Mailing and/or Contact List: Creating a Participants Mailing and/or Contact List: The Limited Query function allows a staff member to retrieve (query) certain information from the Mediated Services system. This information is from

More information

Petrel TIPS&TRICKS from SCM

Petrel TIPS&TRICKS from SCM Petrel TIPS&TRICKS from SCM Knowledge Worth Sharing Histograms and SGS Modeling Histograms are used daily for interpretation, quality control, and modeling in Petrel. This TIPS&TRICKS document briefly

More information